I also am having the same issue but with my Iphone 4S after I upgraded it to IOS 6. Prior to the upgrade I never had any issues with connecting to the wireless network. I also have a I-Touch that I haven't upgraded yet and I have no problems connecting. I have taken my phone into the Apple store and it has no problem connecting to their network. They have reset my network, reinstalled IOS 6 and I bring it home and still can't connect. I have been on the phone with Verizon and Apple together and they can't determine what the issue is. I am going back to the store tomorrow and will let you know if I find out any thing else. There are several different discussions on this site all having to do with not being able to connect to the wireless network after upgrading to IOS 6 which is probably what you have on your Ipad.
Nice to know it's not just me. I'm sure the problem is with my Westell DSL modem/router not talking correctly to the iPad but I can't find anything on the Apple or Verizon sites that's been of much help. I have played with the router configuration and gotten the iPad to connect but then I can't access the internet with either the iPad or my PC and have had to reset the router which puts me back where I started. I did try both enabling and disabling MAC address filtering by the way and that didn't help.
I spoke to Verizon again this morning and they are going to send me a new wireless modum. Once I receive I will let you know if that works or not. The Westell has no issues making a connection to any Apple device that hasn't upgraded to IOS 6 so I'm not sure what has changed in IOS 6 that now makes it not able to communicate with the Westell modum.
Look at iOS Troubleshooting Wi-Fi networks and connections http://support.apple.com/kb/TS1398
iPad: Issues connecting to Wi-Fi networks http://support.apple.com/kb/ts3304
iOS: Recommended settings for Wi-Fi routers and access points http://support.apple.com/kb/HT4199
Additional things to try.
Try this first. Turn Off your iPad. Then turn Off (disconnect power cord for 30 seconds or longer) the wireless router & then back On. Now boot your iPad. Hopefully it will see the WiFi.
Go to Settings>Wi-Fi and turn Off. Then while at Settings>Wi-Fi, turn back On and chose a Network.
Change the channel on your wireless router (Auto or Channel 6 is best). Instructions at http://macintoshhowto.com/advanced/how-to-get-a-good-range-on-your-wireless-netw ork.html
Another thing to try - Go into your router security settings and change from WEP to WPA with AES.
How to Quickly Fix iPad 3 Wi-Fi Reception Problems
If none of the above suggestions work, look at this link.
iPad Wi-Fi Problems: Comprehensive List of Fixes
Fix iPad Wifi Connection and Signal Issues http://www.youtube.com/watch?v=uwWtIG5jUxE
Fix Slow WiFi Issue https://discussions.apple.com/thread/2398063?start=60&tstart=0
Unable to Connect After iOS Update - saw this solution on another post.
Note - When troubleshooting wifi connection problems, don't hold your iPad by hand. There have been a few reports that holding the iPad by hand, seems to attenuate the wifi signal.
If any of the above solutions work, please post back what solved your problem. It will help others with the same problem.
I received the new modum from Verizon and hooked it up today and was able to connect to the wifi right away. You have to tell them that the Westell is not compatable. The ActionTec they sent is a WPA2 security and I know the Westell was a WEP. There has to be something in the IOS 6 that caused the compatablilty issue but what I don't understand is there are open wifi's everywhere and their not all going to work with IOS 6. Apple still needs to make a correction to their software. Good luck and let me know how it goes.
My one friend has had an iPad for a while. I stopped over at his lace last night so he could show me some of the tricks and smooth out the learning curve. I tried my iPad on his wireless connection and at first it didn't work. He has a D-Link modem. We played around a little bit with his iPad which did work on his modem and looked at the IP, DNS, etc settings that the modem was assigning to his iPad. I switched my iPad to manual configuratioin, punched in the data his iPad showed but with the IP address incremented by 1 and it worked. I was able to connect both at his place and at home.
Obviously there's some sort of incompatability issue between the iPad and at least several wi-fi modems that either Verizon or Apple need to address but this manual work-around put a bandaide on my iPad so I can use it to make a wi-fi connection to the Internet.
I may still ask Verizon for a replacement modem.